Adaptation Noise And Self Organizing Systems

We analytically study the dynamics of evolving populations that exhibit metastability on the level of phenotype or fitness. In constant selective environments, such metastable behavior is caused by two qualitatively different mechanisms. One the one hand, populations may become pinned at a local fitness optimum, being separated from higher-fitness genotypes by a {\em fitness barrier} of low-fitness genotypes. On the other hand, the population may only be metastable on the level of phenotype or fitness while, at the same time, diffusing over {\em neutral networks} of selectively neutral genotypes. Metastability occurs in this case because the population is separated from higher-fitness genotypes by an {\em entropy barrier}: The population must explore large portions of these neutral networks before it discovers a rare connection to fitter phenotypes. We derive analytical expressions for the barrier crossing times in both the fitness barrier and entropy barrier regime. In contrast with ``landscape'' evolutionary models, we show that the waiting times to reach higher fitness depend strongly on the width of a fitness barrier and much less on its height. The analysis further shows that crossing entropy barriers is faster by orders of magnitude than fitness barrier crossing. Thus, when populations are trapped in a metastable phenotypic state, they are most likely to escape by crossing an entropy barrier, along a neutral path in genotype space. If no such escape route along a neutral path exists, a population is most likely to cross a fitness barrier where the barrier is {\em narrowest}, rather than where the barrier is shallowest.

In this paper we consider how to organize the sharing of information in a distributed network of sensors and data processors so as to provide explanations for sensor readings with minimal expenditure of energy. We point out that the Minimum Description Length principle provides an approach to information fusion that is more naturally suited to energy minimization than traditional Bayesian approaches. In addition we show that for networks consisting of a large number of identical sensors Kohonen self-organization provides an exact solution to the problem of combining the sensor outputs into minimal description length explanations.

We construct a simple model of a proto-cell that simulates a stochastic dynamics of abstract chemicals on a two-dimensional lattice. We assume that chemicals catalyze their reproduction through interaction with each other, and that between some chemicals repulsion occurs. We have shown that chemicals organize themselves into a cell-like structure that maintains its membranes dynamically. Further, we have obtained cells that can divide themselves automatically into daughter cells.

The noise of signals or currents consisting from a sequence of pulses, elementary events or moving discrete objects (particles) is analyzed. A simple analytically solvable model is investigated in detail both analytically and numerically. It is shown that 1/f noise may result from the statistics of the pulses transit times with random increments of the time intervals between the pulses. The model also serves as a basis for revealing parameter dependences of 1/f noise and allows one to make some generalizations. As a result the intensity of 1/f noise is expressed through the distribution and characteristic functions of the time intervals between the subsequent transit times of the pulses. The conclusion that 1/f noise may result from the clustering of the signal pulses, elementary events or particles can be drawn from the analysis of the model systems.

We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a second-order phase transition. We show that the number of individuals who eventually keep adopting the innovation strongly depends on connectivity between individuals.

The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, the opinion change of the individuals is given by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit holding for fast communication we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) changes the ratio between minority and majority, until above a critical external support the supported subpopulation exists always as a majority. Spatial effects lead to two critical ``social'' temperatures, between which the community exists in a metastable state, thus fluctuations below a certain critical wave number may result in a spatial opinion separation. The range of metastability is particularly determined by a parameter characterizing the individual response to the communication field. In our discussion, we draw analogies to phase transitions in physical systems.

We propose a stochastic dynamic model of migration and economic aggregation in a system of employed (immobile) and unemployed (mobile) agents which respond to local wage gradients. Dependent on the local economic situation, described by a production function which includes cooperative effects, employed agents can become unemployed and vice versa. The spatio-temporal distribution of employed and unemployed agents is investigated both analytically and by means of stochastic computer simulations. We find the establishment of distinct economic centers out of a random initial distribution. The evolution of these centers occurs in two different stages: (i) small economic centers are formed based on the positive feedback of mutual stimulation/cooperation among the agents, (ii) some of the small centers grow at the expense of others, which finally leads to the concentration of the labor force in different extended economic regions. This crossover to large-scale production is accompanied by an increase in the unemployment rate. We observe a stable coexistence between these regions, although they exist in an internal quasistationary non-equilibrium state and still follow a stochastic eigendynamics.

We introduce the Webworld model, which links together the ecological modelling of food web structure with the evolutionary modelling of speciation and extinction events. The model describes dynamics of ecological communities on an evolutionary timescale. Species are defined as sets of characteristic features, and these features are used to determine interaction scores between species. A simple rule is used to transfer resources from the external environment through the food web to each of the species, and to determine mean population sizes. A time step in the model represents a speciation event. A new species is added with features similar to those of one of the existing species and a new food web structure is then calculated. The new species may (i) add stably to the web, (ii) become extinct immediately because it is poorly adapted, or (iii) cause one or more other species to become extinct due to competition for resources. We measure various properties of the model webs and compare these with data on real food webs. These properties include the proportions of basal, intermediate and top species, the number of links per species and the number of trophic levels. We also study the evolutionary dynamics of the model ecosystem by following the fluctuations in the total number of species in the web. Extinction avalanches occur when novel organisms arise which are significantly better adapted than existing ones. We discuss these results in relation to the observed extinction events in the fossil record, and to the theory of self-organized criticality.

We review recent work aimed at modeling species extinction over geological time. We discuss a number of models which, rather than dealing with the direct causes of particular extinction events, attempt to predict overall statistical trends, such as the relative frequencies of large and small extinctions, or the distribution of the lifetimes of species, genera or higher taxa. We also describe the available fossil and other data, and compare the trends visible in these data with the predictions of the models.

We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable beams. Particles are allowed to be convex or concave. We present first results of simulations using this particle model.